Mesoscale Boundary Layer and Heat Flux Variations over Pack Ice

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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
VOLUME 47
Mesoscale Boundary Layer and Heat Flux Variations over Pack Ice–Covered
Lake Erie
MATHIEU R. GERBUSH*
Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
DAVID A. R. KRISTOVICH
Center for Atmospheric Science, Illinois State Water Survey, Illinois Department of Natural Resources, Champaign, Illinois
NEIL F. LAIRD
Department of Geoscience, Hobart and William Smith Colleges, Geneva, New York
(Manuscript received 17 April 2006, in final form 7 March 2007)
ABSTRACT
The development of extensive pack ice fields on the Great Lakes significantly influences lake-effect
storms and local airmass modification, as well as the regional hydrologic cycle and lake water levels. The
evolution of the ice fields and their impacts on the atmospheric boundary layer complicates weather
forecasters’ ability to accurately predict late-season lake-effect snows. The Great Lakes Ice Cover–
Atmospheric Flux (GLICAF) experiment was conducted over Lake Erie during February 2004 to investigate the surface–atmosphere exchanges that occur over midlatitude ice-covered lakes. GLICAF observations taken by the University of Wyoming King Air on 26 February 2004 show a strong mesoscale thermal
link between the lake surface and the overlying atmospheric boundary layer. Mesoscale atmospheric variations that developed over the lake in turn influenced heat exchanges with the surface. Boundary layer
sensible and latent heat fluxes exhibited different relationships to variations in surface pack ice concentration. Turbulent sensible heat fluxes decreased nonlinearly with increases in underlying lake-surface ice
concentration such that the largest decreases occurred when ice concentrations were greater than 70%.
Latent heat fluxes tended to decrease linearly with increasing ice concentration and had a reduced correlation. Most current operational numerical weather prediction models use simple algorithms to represent
the influence of heterogeneous ice cover on heat and moisture fluxes. The GLICAF findings from 26
February 2004 suggest that some currently used and planned approaches in numerical weather prediction
models may significantly underestimate sensible heat fluxes in regions of high-concentration ice cover,
leading to underpredictions of the local modification of air masses and lake-effect snows.
1. Introduction
The presence of substantial pack ice cover on the
Great Lakes significantly modifies the local and largescale atmospheric response to the lakes (e.g., Niziol
* Current affiliation: Office of the New Jersey State Climatologist, Rutgers, The State University of New Jersey, Piscataway,
New Jersey.
Corresponding author address: Dr. David A. R. Kristovich,
2204 Griffith Dr., Champaign, IL 61820-7495.
E-mail: dkristo@uiuc.edu
DOI: 10.1175/2007JAMC1479.1
© 2008 American Meteorological Society
1987). Although the presence of pack ice reduces the
transfer of heat and moisture from the lake surface to
the atmosphere, lake-effect clouds and precipitation
have occurred during conditions of extensive ice coverage (R. LaPlante, Cleveland National Weather Service Forecast Office, 2003, personal communication;
see also Buffalo National Weather Service Forecast Office 2005 at http://www.erh.noaa.gov/buf/lakeffect/
indexlk.html; Laird and Kristovich 2004). A recent
study by Cordeira and Laird (2005) examined the evolution of snowfall regions and ice-cover conditions for
two noteworthy lake-effect snowfall events over the
eastern Great Lakes when ice concentrations were
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GERBUSH ET AL.
greater than 90% for most of Lake Erie. For example,
during one of the events examined (28–31 January
2004), snowfall totals downwind of Lake Erie exceeded
30 cm. These observations indicate that substantial sensible and latent heat fluxes can still occur over Great
Lakes that are substantially covered with pack ice.
Studies of Great Lakes winter lake-effect processes
have typically examined the mesoscale and microphysical atmospheric boundary layer responses to surface
diabatic forcing over ice-free regions (e.g., Kristovich et
al. 1999, 2000, 2003; Young et al. 2000; Cooper et al.
2000; Mayor et al. 2003; Schroeder et al. 2006; Miles and
Verlinde 2005a,b) and the large-scale collective influence of the lakes (e.g., Sousounis and Fritsch 1994; Angel and Isard 1997; Sousounis 1997, 1998; Weiss and
Sousounis 1999). There have been only a few lake-effect studies that have investigated the atmospheric response to variations in lake-surface characteristics. For
example, Kristovich and Laird (1998) indicated that
spatial variations in Lake Michigan lake-surface temperature influenced the location of initial cloud development in the lake-effect boundary layer, suggesting
that lake-surface temperature heterogeneities can noticeably influence lake–atmosphere heat exchange and
convective boundary layer development over the Great
Lakes. Kristovich et al. (2001) observed that local variations in lake-surface temperature influenced mesoscale
patterns of surface heat fluxes. The presence of pack ice
would be expected to influence both the surface temperature fields and roughness, in turn having a significant impact on heat and moisture fluxes.
Investigations examining surface heat fluxes and the
boundary layer response over ice-covered water have
largely been confined to high-latitude or Arctic regions
(e.g., Andreas et al. 1979; Alam and Curry 1995, 1997;
Pinto et al. 1995; Andreas and Cash 1999; Rouse et al.
2003; Zulauf and Krueger 2003) or marginal oceanic ice
shelves (e.g., Renfrew and Moore 1999; Krahmann et
al. 2003). Wintertime ice-cover conditions in Arctic regions tend to be characterized by extensive thick ice
with near-zero surface heat fluxes and a few leads of
open water encompassing a small percentage of the surface area, but associated with large surface heat fluxes.
Wintertime sea–air temperature differences can range
from 20° to 40°C over leads; thus, breaks in Arctic ice
cover are a major contributor to the Arctic heat budget
(e.g., Alam and Curry 1997). The magnitude of the influence of leads on the arctic boundary layer depends
on numerous factors, including air–ocean temperature
differences, lead size and orientation relative to the
low-level wind direction, wave age, water surface cooling rates, atmospheric stability, and low-level wind
speed and shear (e.g., Alam and Curry 1997; Pinto et al.
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1995; Zulauf and Krueger 2003). A key difficulty in
applying results from Arctic studies to midlatitudes is
that there are significant differences in typical wintertime environmental and surface conditions (e.g., lake–
air temperature difference, near-surface static stability,
and thickness of ice fields). In addition, many of the
processes known to influence surface–air exchanges depend on factors not routinely monitored and therefore
are not readily available for incorporation into operational weather prediction models.
Most of the ice cover over the Great Lakes is composed of pack ice, which tends to peak in coverage in
late February–early March (Assel 1999). The variability
of weather conditions in the Great Lakes, with the passage of polar fronts and cyclones accompanied by high
winds, precipitation, and air masses of varying origins,
can result in considerable ice formation and loss. In
midlake areas, pack ice movement, compaction, formation, and melt can result in highly transitory ice configurations. In addition, variability in atmospheric conditions not only affects ice characteristics, but also leads
to a large range in surface heat fluxes (Laird and Kristovich 2002). The variability in both surface and atmospheric conditions plays an important role in coldseason weather conditions, underscoring the need for
adequate representations of surface-interaction processes in mesoscale numerical weather prediction models.
Many numerical weather prediction models currently
utilize a simplified treatment of Great Lakes ice
cover and can have difficulties accurately predicting
lake-effect events when extensive ice cover is present
(R. LaPlante, Cleveland National Weather Service Office, 2003, personal communication; T. Niziol, Buffalo
National Weather Service Office, 2004, personal communication). For instance, the North American Mesoscale (NAM) Model designates 12-km lake grid boxes
with less than 50% ice concentration as open water (i.e.,
no lake ice). Grid boxes with greater than 50% ice
concentration are considered to be fully covered with
1-m-thick ice (Meteorology Education & Training
2006). Previously unavailable field observations of the
boundary layer response to Great Lakes ice cover are
needed to facilitate improved winter weather forecasting in the Great Lakes region. The Great Lakes Ice
Cover–Atmospheric Flux (GLICAF) experiment was
conducted with a primary goal of using aircraft to collect unprecedented boundary layer observations over a
pack ice–covered Lake Erie.
This paper describes the data collection during
GLICAF and analysis techniques in section 2, presents
the observed relationships between ice cover and
boundary layer properties and heat fluxes in section 3,
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and discusses the findings in the context of previous
studies and numerical weather prediction in section 4.
2. Data and methods
This study utilizes a unique dataset for the Great
Lakes area to quantify the surface–atmosphere heat exchanges that occur over midlatitude pack ice–covered
lakes. This section describes the field data collection
and analysis techniques employed to understand these
exchanges.
a. Data
During February 2004, the University of Wyoming
King Air aircraft conducted research flights over Lake
Erie in support of the GLICAF experiment. GLICAF
operations were centered in Toledo, Ohio. Five intensive operations periods (IOPs) were conducted. Flight
stacks were flown approximately perpendicular to the
mean boundary layer wind and were composed of one
upper-level (near 500-m altitude) and two low-level
(near 45-m altitude) flight legs. Upper-level flight legs
were performed to survey ice-cover conditions using a
digital video camera and a downward-pointing pyrometer, while the low-level flight legs (hereinafter referred
to as “flux legs”) were utilized to collect turbulent heat
flux measurements. Individual flight legs in each flight
stack are identified chronologically (i.e., CD2 is the second flight leg in stack CD).
The current study focuses on the 26 February 2004
IOP, during which there was in-flight evidence of positive sensible and latent heat fluxes and generally good
low-level visibilities (required for pack ice observations). Four flight stacks were performed in total, with
two conducted during the morning and the remaining
two occurring during the afternoon. The Aqua Moderate Resolution Imaging Spectroradiometer (MODIS)
image of the study area at 1815 UTC (Fig. 1a) shows the
spatial ice-cover distribution and the locations of flight
stacks performed on 26 February. The large-scale icecover features are consistent with the 26 February National Ice Center ice-cover analysis (see Great Lakes
ice analysis 2004, available online at http://www.natice.
noaa.gov; Fig. 1b), with high-concentration ice in the
vicinity and east of flight stack CD, particularly in
southern regions. Lower-concentration ice was located
near stack AB, and ice-free water along the entire
northern and western portions of the lake. A segment
of flight stack AB had low-level stratus and fog, which
obscured observations of surface pack ice. In addition,
melting of the ice surface during the afternoon flight
stacks (EF and GH) precluded their use for the present
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study. Portions of the flight stacks used for the current
investigation are highlighted with solid black lines in
Fig. 1a.
During the GLICAF experiment, observations of
surface pack ice concentration and turbulent heat
fluxes (sensible and latent) were obtained over regions
of variable ice concentration. King Air data were available at frequencies of 1 and 25 Hz, corresponding to
flight distances of approximately 80 and 3 m, respectively. Temperature and water vapor pressure measurements were collected by the Minco Element Reverse
Flow thermometer and the Li-Cor, Inc., Model LI-6262
CO2/H2O Analyzer, correspondingly (University of
Wyoming 2005). Flight-level vertical air motions were
observed by the University of Wyoming King Air gust
probe (see, e.g., Lenschow 1973).
Ice concentration estimates were retrieved primarily
by a downward-pointing Heimann KT-19.85 pyrometer, with supporting data from a digital video camera.
This pyrometer measures upward-directed infrared radiation from which surface temperatures can be inferred. The Heimann pyrometer operated with a spectral range of 9.6–11.5 ␮m, a field-of-view of 2°, and a
measurement range from ⫺50° to 400°C and possessed
an adjustable response time that was set at 0.1 s for this
experiment (Laursen 2005; University of Wyoming
2005). Comparisons between pyrometer surface temperature data and digital video imagery (collected using
a JVC, Inc., GR-DV800U video camera) show that
lake-surface ice and water, as well as boundaries between ice and water, were well depicted by the pyrometer during the morning flight (stacks AB and CD).
Figure 2 shows an example of responses of pyrometer
measurements collected over water and ice surface
transitions. During the morning hours, areas of water
and ice cover were generally associated with surface
temperatures of greater than and less than ⫺0.5°C, respectively. Examination of inferred pack ice concentrations using thresholds between ⫺0.1° and ⫺0.9°C resulted in changes in values of ice concentrations, but did
not change the overall shapes of the relationships (e.g.,
linear versus nonlinear) between ice-cover concentration and heat fluxes. For the present study, lake-surface
ice concentration was estimated by the percentage of
25-Hz Heimann pyrometer observations below ⫺0.5°C
over the same time periods used for flux calculations.
b. Methods
Turbulent sensible and latent heat fluxes were estimated using eddy-correlation techniques (e.g., Stull
1988). Sensible heat flux was calculated using
H ⫽ ␳cp共w⬘␪⬘兲,
共1兲
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GERBUSH ET AL.
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FIG. 1. (a) Aqua MODIS 250-m resolution image of ice cover on Lake Erie from 1815 UTC 26 Feb 2004.
Locations of flight stacks AB, CD, EF, and GH, conducted by the University of Wyoming King Air on this date,
are indicated. Thick, solid lines indicate portions of the flight stacks used in the current study. The approximate
45-m wind direction observed by the King Air during flight stacks AB and CD is shown. (b) Portion of the National
Ice Center ice analysis for this date (see http://www.natice.noaa.gov).
where ␳ represents the density of dry air at 0°C temperature and 1000-hPa pressure (1.275 kg m⫺3), cp is
the specific heat of dry air at constant pressure (1004 J
K⫺1 kg⫺1), w⬘ represents perturbations in vertical wind
speed, and ␪⬘ represents perturbations in potential temperature. Similarly, latent heat flux was determined using
HL ⫽ ␳L␷ 共w⬘q⬘兲,
共2兲
where L␷ is the latent heat of vaporization (2.5 ⫻ 106 J
kg⫺1) and q⬘ represents perturbations in specific hu-
midity. Similar methods have been successfully employed in several studies of positive heat fluxes in lakeeffect situations using University of Wyoming King Air
collected data (e.g., Kelly 1984; Chang and Braham
1991; Kristovich 1993; Kristovich and Braham 1998;
Kristovich et al. 2003).
To calculate heat fluxes, it is necessary to determine
perturbations in potential temperature and specific humidity using appropriate mean values. Various methods have been used to determine mean values, including linear detrending (e.g., Kristovich 1993; Kristovich
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and Braham 1998), mean values for blocks of time periods and running mean values (Sun et al. 1996), and
high-pass filtering techniques (e.g., Chang and Braham
1991). Temperature and specific humidity varied nonlinearly along flux legs in flight stacks AB and CD,
making linear-detrending and block-averaging techniques inappropriate. For this study, ␪⬘ and q⬘ were
calculated by subtracting 30-s moving averages (i.e.,
running means) from instantaneous values of ␪ and q. It
is recognized that running means do not satisfy Reynolds averaging criteria because the mean values are different for each point along the time series. Despite this,
however, Sun et al. (1996) found that the method was
very useful in cases with highly nonlinear trends of state
variables. Pass-mean sensible heat fluxes calculated
with data detrended using running means agreed well
with those estimated using bulk methods. Calculated
latent heat fluxes tended to be of equal sign but less
magnitude than expected using bulk methods.
3. Results
a. Synoptic weather and ice-cover conditions
FIG. 2. Example of (b) 25-Hz Heimann pyrometer measurements (°C) and (a), (c) digital video images over two lake-surface
ice water boundaries during flight leg CD1. The arrows in the
pyrometer time series correspond to the times of the video images
in (a) and (c). The King Air was flying from bottom to top in the
video images. The King Air flew approximately 3.5 km over the
time interval shown.
During the morning of 26 February, regional weather
conditions were dominated by a 1039-hPa surface high
pressure system located east of Hudson Bay in Quebec,
Canada. At 850 hPa, an area of high geopotential
heights was centered over southern Lake Huron, to the
north of the study region. The associated anticyclonic
flow around the regions of high pressure resulted in
winds generally from the ENE between the surface and
850 hPa throughout the study day. Cloud cover was
sparse, though high-level cirrus clouds occasionally
drifted over the study area. Patches of dense fog were
also present, particularly along the southern shore of
Lake Erie. The presence of low clouds obscured the
lake surface during portions of these flight legs, making
it impossible to estimate lake-surface ice concentration.
Approximately 25 and 32 km of data from the southern
ends of the two flux legs in flight stack AB were not
analyzed for this reason. Since fog was not detected
along any other portions of the flux legs, all remaining
data were retained.
Horizontal wind speeds observed by the King Air
during flux legs ranged from 3 to 10 m s⫺1. Flux-level
temperatures from stacks AB and CD mostly ranged
from ⫺3.5° to ⫺1°C, resulting in flux leg–average differences in temperature between the lake surface and
near-surface air temperature (estimated by dry adiabatic adjustment of flux-level temperatures) of around
0.3°C in stack AB and 0.8°C in stack CD. With moderate winds and positive lake–air temperature differences, weak upward surface heat fluxes were anticipat-
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ed. Bulk estimates using aircraft observations collected
during flux legs in flight stacks AB and CD ranged from
1.7 to 7.1 W m⫺2 for sensible heat fluxes and 3.9 to 11.6
W m⫺2 for latent heat fluxes (Gerbush 2005). Observed
average sensible heat fluxes during the flux legs agreed
well with bulk estimates, ranging from 1.8 to 6.1 W m⫺2.
Latent heat fluxes, however, were lower than expected,
ranging from 1.2 to 3.7 W m⫺2.
An ice-cover analysis provided by the U.S. National
Ice Center (Fig. 1b) indicated that substantial ice cover
(⬎90%) was present over the majority of Lake Erie on
26 February 2004. The ice-cover analysis presented a
similar spatial ice-cover distribution as the MODIS image shown in Fig. 1a. The highest concentration ice
cover was generally confined to eastern portions of the
lake, with greater ice concentration variability in the
central and western basin where regions of ice-free water were present, especially along the southern and
northern shores of the lake.
b. Relationships between lake-surface and low-level
atmospheric conditions
Turbulent heat fluxes depend on both surface characteristics and near-surface atmospheric thermodynamic properties. Atmospheric conditions observed
during the King Air flux legs (near 45-m altitude) were
used to estimate near-surface temperature and humidity conditions to better understand their relationship
with changes in the lake surface as well as to give background information necessary for understanding observations of heat fluxes discussed later.
Figure 3 shows lake-surface temperature, as determined by the Heimann pyrometer, and air temperatures observed by the King Air during a flux leg in each
of the flight stacks AB and CD. Similar spatial patterns
were seen in the other flux legs. Spatial patterns in
lake-surface and 45-m air temperature display strong
similarities, especially with respect to mesoscale (⬎5
km) variations. The general increasing trend in lakesurface temperatures from south to north along flight
leg AB1 is matched by a similar northward increase in
45-m air temperatures (Fig. 3a). A significant mesoscale
trend in lake-surface temperature (increase of around
2.5°C from south to north) was also present along flight
leg CD2 (Fig. 3b). Mesoscale variations in lake-surface
characteristics appear to play a dominant role in determining mesoscale variations in low-level atmospheric
temperatures, despite the presence of extensive ice
cover, as discussed later.
Alternatively, small-scale (⬍5 km) variations in lakesurface temperatures were not well correlated with
flux-level temperature variations. For instance, smallscale variations in lake-surface temperatures (abrupt
FIG. 3. Time series of Heimann radiometric surface temperature (black) and 45-m air temperature (gray) for flux legs (a) AB1
and (b) CD2. Here, “S” and “N” denote the southern and northern endpoints of the passes, respectively. Time is in hours and
minutes, UTC.
surface temperature fluctuations of 1.5°–2°C in less
than 1 km) along the southern half of flight leg AB1 did
not appear to correlate with similar variations in 45-m
air temperatures (Fig. 3a). In flight leg CD2 (Fig. 3b),
fewer small-scale surface temperature fluctuations were
evident, but those present were also not consistently
reflected in air temperatures at a height of 45 m.
Figure 4 shows estimates of lake-surface water vapor
mixing ratio and 45-m atmospheric mixing ratio observed during flux legs AB1 and CD2. Surface mixing
ratios were approximated by calculating the saturation
mixing ratio (over a plane water surface) as a function
of lake-surface temperature under the assumption that
the air at the lake surface was the same temperature as
the surface and saturated with respect to water. The
saturation mixing ratio over ice cover should be reasonably approximated by the saturation mixing ratio
estimated assuming a water surface since pyrometerobserved lake-surface temperatures were generally
close to 0°C.
Large-scale variations in surface mixing ratio showed
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FIG. 4. Time series of estimated saturation mixing ratio (black),
calculated from Heimann radiometric temperature observations,
and 45-m mixing ratio (gray) for flux legs (a) AB1 and (b) CD2.
Here, “S” and “N” denote the southern and northern endpoints of
the passes, respectively.
a relatively weak correlation with 45-m mixing ratio. In
flight leg AB1, where surface mixing ratios generally
increased from south to north, flux-level mixing ratio
observations exhibited a slight decreasing trend (Fig.
4a). For flight leg CD2, the mixing ratio observed at
45-m height (Fig. 4b) exhibited an overall south-tonorth increasing trend (approximately 0.25 g kg⫺1), but
at a much slower rate of increase than at the surface
(around 0.60 g kg⫺1). As was the case for temperature,
the small-scale variations in surface mixing ratio in both
stacks were not observed in the 45-m mixing ratio observations. The stronger relationship between lakesurface and 45-m temperatures relative to the correspondence in mixing ratios at both heights suggests that
sensible heat fluxes may possess a stronger relationship
with variations in surface ice concentration than latent
heat fluxes for the present case.
c. Relationships between surface ice concentrations
and heat fluxes
Since low-level atmospheric conditions were related
to mesoscale lake-surface characteristics, it is antici-
VOLUME 47
FIG. 5. Time series of 30-s average heat fluxes (open squares)
and lake-surface temperatures calculated from Heimann radiometric observations (closed dots) taken during flight leg CD2, 26
Feb 2004. (a) Sensible heat fluxes; (b) latent heat fluxes. Here, “S”
and “N” denote the southern and northern endpoints of the
passes, respectively. Each 30-s data point represents approximately a 2.4-km flight distance.
pated that heat fluxes would also be influenced by lakesurface pack ice concentrations. Figure 5 gives time series of 30-s-average (approximately 2.4-km flight distance) heat fluxes and surface temperatures as the King
Air flew from south to north in flight leg CD2. Both
sensible and latent heat fluxes increased from the
colder southern regions with high ice concentrations to
the warmer northern regions with lower ice concentration. This overall south-to-north increasing trend illustrates the influence of regional variations in ice concentration on sensible heat fluxes. However, there is considerable spatial variability in both heat flux and
surface temperature observations along the flight track.
Figure 6 shows the relationships between sensible
heat fluxes and surface pack ice concentrations for both
flux legs in flight stack CD, calculated over intervals
of 15 s (about 1.2-km flight length), 30 s (2.4 km), and
45 s (3.6 km). Although substantial variability is exhibited regardless of averaging interval, decreases in ice
concentration were generally associated with increases
in sensible heat fluxes. For larger flux-averaging scales
(30 and 45 s), the scatter among flux values is reduced.
Data shown in Fig. 6, particularly for larger averaging
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from 100% to 70%, sensible heat flux magnitudes increased and remained nearly unchanged for concentrations less than 70%. To quantify the degree of nonlinearity, we fit a one-phase exponential association
model to the sensible heat flux–ice concentration observations. The basic form of the model equation can be
written as
Y ⫽ ymin ⫹ 共ymax ⫺ ymin兲共1 ⫺ e⫺bX兲,
共3兲
where X and Y are the independent and dependent
variables, respectively, ymax is the plateau of the curve,
ymin is the base of the curve, and b is the exponential
constant (Motulsky and Christopoulos 2003). In the
present case, X is defined as the lake-surface water
concentration (100% minus ice concentration), Y is the
sensible heat flux, ymax is the maximum sensible heat
flux (flux at 0% ice concentration), and ymin is the minimum sensible heat flux (flux at 100% ice concentration). Rewriting Eq. (3) in terms of ice concentration
and sensible heat flux yields
H ⫽ H100% ⫹ 共H0% ⫺ H100%兲关1 ⫺ e⫺b共100⫺I兲兴,
共4兲
FIG. 6. Turbulent sensible heat fluxes from flux legs in stack CD
plotted as a function of lake-surface ice concentration for flux
averaging scales of (a) 15, (b) 30, and (c) 45 s. Best-fit nonlinear
regression curves are also shown in each example.
distances (30 and 45 s), suggest that the relationships
between ice concentration and turbulent sensible heat
fluxes are best represented by a nonlinear model. If a
linear model were used to fit the 30-s average data (Fig.
6b), there would be a tendency for positive residuals
between ice concentrations of about 50% and 90% (not
shown); this violates assumptions for the applicability
of linear regression. As ice concentration decreased
where H0% and H100% are the sensible heat fluxes at
0% and 100% ice concentrations, respectively, and I is
the lake-surface ice concentration (in percent). It is important to note that with the use of this equation for
fitting the observed values, we do not preclude the possibility of a linear relationship (which was found in
some cases, as discussed later).
Resulting regressions for a range of averaging scales
between 15 and 60 s for stacks AB and CD are shown
in Fig. 7. The regressions for stack AB are similar to
each other, although the curves for smaller averaging
scales (such as 15 s) approach a more linear relationship. Regressions for stack CD show nonlinear relationships for the range of averaging scales. The general
agreement between regressions for different flux-averaging scales within each stack suggests the choice of
flux-averaging scale does not strongly affect the nonlinear representation of the relationships. Therefore,
this study reports the findings using regressions based
on 45-s flux averaging (approximately 3.6-km flight distance) for each stack, a scaling period that represents
the approximate mean characteristics of the ensemble
of regressions. Regression parameters for the 45-s
averaging scale for stacks AB and CD are given in
Table 1.
The model parameters listed in Table 1 show substantial differences between the ice concentration–sensible heat flux relationships in stacks AB and CD. Both
H0% and H100% values are larger in stack CD; H100% for
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FIG. 7. Best-fit nonlinear regressions of sensible heat flux as a function of ice concentration
for flux-averaging scales ranging from 15 to 60 s. Flight stack (AB or CD) and flux-averaging
scale for each curve are indicated. In addition, R2 values are given for each averaging scale.
stack AB is close to zero, implying that little heat transfer from the lake to the atmosphere occurred at 100%
ice concentration. For stack CD, a positive H100% value
suggests that weak upward sensible heat fluxes were
present for ice concentrations of 100%. An examination of sensible heat flux observations in Fig. 6 shows
that sensible heat fluxes in stack CD were often greater
than 0 W m⫺2 at 100% ice concentration. The larger
value of b in stack CD than stack AB indicates a larger
increase in sensible heat fluxes with decreasing ice concentration, especially for ice concentrations greater
than 70% in stack CD (Fig. 7). Possible reasons for the
differences in the sensible heat flux and ice concentration relations between stacks are discussed in section 4.
Measurements of latent heat fluxes over different ice
concentrations indicate that they increased steadily
with decreasing ice concentration (Fig. 8). Latent heat
flux values from stack CD generally clustered between
1 and 4 W m⫺2 for ice concentrations above 90%. Latent heat flux values at the highest observed ice concentrations in stack AB (not shown) tended to be clustered around 1 W m⫺2, but were more widely scattered
at lower ice concentrations. For both flight stacks AB
and CD, latent heat fluxes exhibited more variability at
lower ice concentrations (below 90%). For the sake of
remaining consistent with the methods used to quantify
the ice concentration–sensible heat flux relationships,
the same nonlinear model was initially applied to latent
heat flux data. This approach, however, yielded nearlinear regressions for most flux-averaging scales, sug-
gesting that ice concentration–latent heat flux relationships in this case are better represented by a linear
regression model.
Figure 9 shows best-fit regressions of ice concentration–latent heat flux relationships for stacks AB and
CD for a range of averaging scales between 15 and 60 s.
Latent heat flux relationships in stack AB indicate that
minimal moisture exchange occurred at ice concentrations near 100%. For stack CD, the regressions show
that estimated latent heat fluxes over regions of near100% ice concentration were near 2 W m⫺2. Despite
the overall larger latent heat fluxes observed in stack
CD, the slopes of the regressions between flight stacks
are very similar. Table 2 shows the linear regression
model parameters from the 45-s flux-averaging scale,
the most representative of the ice concentration–latent
heat flux relationships shown in Fig. 9. Interpretation of
the differences in pack ice concentration relationships
between sensible and latent heat fluxes, and between
flight stacks, are discussed below.
TABLE 1. Nonlinear regression model parameters for flight
stacks AB and CD derived from turbulent sensible heat fluxes
calculated using a flux-averaging scale of 45 s. These parameters
are for the model Eq. (4).
⫺2
H100% (W m )
H0% (W m⫺2)
b
AB
CD
⫺0.24
3.1
0.031
1.12
5.9
0.077
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677
Erie or over land areas north and south of the flight
stacks. Modification of the air by the lake surface must
have been responsible for the development of this overlake temperature gradient. As illustrated in Fig. 10, airflow along southern regions of Lake Erie experienced a
fetch over areas of high pack ice concentration. The ice
would be expected to limit east-to-west warming of the
air as it flowed over the slightly warmer lake. Farther
north, a fetch over lower ice concentrations would allow for more warming of the air, resulting in the observed south-to-north increase in temperature.
Atmospheric moisture content does not appear to
relate to lake-surface characteristics as directly as temperature. Over southern regions, a greater overlake
fetch would give more opportunity for moistening of
the relatively dry air originating over upwind land areas. However, the smaller overlake fetch in northern
areas may have been offset, to an extent, by the presence of abundant open water, resulting in more rapid
moistening. The resulting gradients at 45-m height and
the surface were not as strongly related for the mixing
ratio (Fig. 4) as they were for temperature (Fig. 3).
Regardless of the reason, this suggests that sensible
heat fluxes would have a stronger relationship with ice
concentration than latent heat fluxes in the current
case.
Clearly, the spatial distribution of pack ice played a
large role in influencing mesoscale variations in temperature and atmospheric moisture in the boundary
layer. As will be discussed below, mesoscale air and
lake-surface condition variability in turn appeared to
influence small-scale variations in sensible and latent
heat fluxes.
b. Contributions to heat fluxes
FIG. 8. Turbulent latent heat fluxes from flux legs in stack CD
plotted as a function of lake-surface ice concentration for flux
averaging scales of (a) 15, (b) 30, and (c) 45 s. Best-fit linear
regression lines are also shown in each example.
4. Discussion
a. Mesoscale variations in surface and atmospheric
conditions
Flux-level observations taken by the University of
Wyoming King Air indicated a south-to-north increase
in air temperature over Lake Erie (see, e.g., Fig. 3).
Regional surface observations provide no indication of
a south-to-north temperature gradient upwind of Lake
It is interesting to note that the magnitude of heat
fluxes differs between flight stacks AB and CD. To a
first approximation, sensible heat fluxes are proportional to near-surface wind speed and the temperature
difference between the lake surface and the overlying
air, ⌬Tlake–air (e.g., Garratt 1992). Stack-mean sensible
heat fluxes in CD were approximately 2.4 times those in
stack AB. Mean flux-level wind speeds were about 30%
greater in stack CD than in stack AB, suggesting that
differences in wind speed alone were not enough to
explain the larger positive sensible heat fluxes observed
during the stack CD. Differences between surface air
temperature (estimated by adjusting 45-m air temperatures dry adiabatically to the surface) and pyrometerdetected lake-surface temperatures were also greater in
stack CD than in AB. A mean ⌬Tlake–air of 0.80°C during stack CD was more than 2 times as large as the
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VOLUME 47
FIG. 9. Best-fit linear regressions of latent heat flux as a function of ice concentration for
flux-averaging scales ranging from 15 to 60 s. Flight stack (AB or CD) and flux-averaging scale
for each curve are indicated. In addition, R2 values are given for each averaging scale.
mean ⌬Tlake–air of 0.32°C in stack AB. Consequently,
overall differences in ⌬Tlake–air between stack AB and
CD were primarily responsible for the stronger passmean sensible heat fluxes observed in stack CD, with
increases in wind speed playing a secondary role.
One factor that contributed to a larger mean ⌬Tlake–air
in stack CD was a region of cold air and higher ice
concentrations along the southern portion of the stack
CD flux legs (Fig. 3b), which resulted in locally higher
values of ⌬Tlake–air. A similar area of cold air was also
present in the southern segment of stack AB, but is not
evident in Fig. 3a because it was removed from the
analyses because of the presence of low clouds along
the flight path. The importance of this area of slightly
cooler air on heat flux relationships highlights the
strong sensitivity of surface–atmosphere exchanges to
mesoscale variations in atmospheric thermodynamic
conditions, common in the Great Lakes region during
winter.
heat fluxes rapidly decreased as ice concentrations increased above about 70% and were nearly constant for
lower ice concentrations. Latent heat fluxes tended to
decrease linearly with increases in ice concentration,
suggesting that latent heat fluxes did not respond
strongly to small breaks in high ice concentration areas.
Despite the general relationships between heat fluxes
and the surface, there is a great deal of scatter in the
observations. This scatter might be interpreted as being
due, in part, to random variations in turbulent eddies
responsible for transporting heat and moisture vertically. However, some of the scatter likely reflects physical processes linking the surface to atmospheric conditions at the 45-m-altitude aircraft observations. As described in Hechtel et al. (1990), variations in heat and
moisture transfers resulting from small-scale surface
features would be expected to combine to create smallscale internal boundary layers that grow upward into
the boundary layer.
c. Ice concentration–heat flux relationships
TABLE 2. Linear regression model parameters for flight stacks
AB and CD derived from turbulent latent heat fluxes calculated
using a flux-averaging scale of 45 s.
A noteworthy finding from an analysis of data collected on 26 February 2004 during the GLICAF experiment was that sensible heat fluxes varied nonlinearly
and latent heat fluxes varied linearly with surface pack
ice concentration over Lake Erie. Turbulent sensible
Slope
Y intercept
AB
CD
⫺0.027
2.78
⫺0.034
5.26
FEBRUARY 2008
GERBUSH ET AL.
679
FIG. 10. Schematic representation of mesoscale regions of warmer and colder air in relation
to surface land, water, and pack ice locations. Approximate locations of data used from flight
stacks AB and CD are indicated. Surface imagery is from MODIS, as described in Fig. 1.
To gain insight into whether such small-scale internal
boundary layers from the surface influence the observations at 45-m height, Fig. 11 shows 1-Hz fluxes for
areas of relatively cool and warm air temperatures measured along flux leg CD2. Similar findings were seen for
CD3 and flux legs in stack AB (with the exception that
the cooler area in stack AB was removed from consideration for this study because of low-level clouds). In
the cooler region, 1-Hz sensible heat fluxes tended to
exhibit peak values over and near regions of warmer
FIG. 11. One-second average fluxes (open boxes) and lake-surface temperatures (solid diamonds) observed during King Air pass CD2
on 26 Feb 2004. From a (top) portion of the pass with relatively cool air temperatures and (bottom) warmer portion of the pass. Air
temperatures for the entire pass are shown in Fig. 3b. The 1-s average fluxes with the largest magnitudes are circled. One minute is
approximately equal to a 4.8-km flight distance.
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surface temperatures (Fig. 11a). However, in the
warmer area this relationship was not as obvious (Fig.
11c). We hypothesize that this is due to the locally
larger lake–air temperature differences over leads in
the cooler region as compared with the warmer region.
Regardless of the reasons, these observations confirm
differences in the relationship between sensible heat
fluxes and the surface conditions in the cold, high ice
concentration region when compared with the warm,
low ice concentration regions, as suggested by the nonlinear relationships discussed in section 3c (and shown
in Figs. 6, 7). Latent heat fluxes, on the other hand, did
not appear to be closely related to small-scale peaks in
surface temperatures in either the cool or warm regions. This is consistent with earlier findings that latent
heat fluxes did not respond as strongly as sensible heat
fluxes to small-scale areas of warm surface temperature
(interpreted as leads) in regions of high-concentration
pack ice.
While it is not possible to fully explain with this
dataset why sensible and latent heat fluxes vary differently with surface ice concentrations, we speculate that
nearly the same amount of water vapor would be available for vertical transport over water as over ice at air
temperatures close to 0°C. For example, saturation vapor pressure over ice would be approximately 97%–
99% of that over water over the typical range of lakesurface temperatures observed in this case (from ⫺3° to
⫺1°C). We speculate that even weak transfers of moisture between the lake and atmosphere over high concentration ice may decrease the local responses in latent heat fluxes over small breaks in ice cover, resulting
in more linear relationships between fluxes and pack
ice concentration.
d. Implications for late-winter lake-effect snow
prediction
The nonlinear relationship between sensible heat
fluxes and surface ice concentrations appears to be the
result of mesoscale variations in both ice cover and
atmospheric conditions along the flight legs, as well as
the upwind surface–atmosphere interactions that influenced atmospheric conditions where aircraft observations were collected. If found to be a common feature,
the nonlinear relationship would have important implications for mesoscale operational forecast models. For
example, Fig. 12 schematically compares the relationships found from the analysis of the 26 February 2004
GLICAF measurements with the NAM Model’s representation of sensible heat fluxes as a function of ice
concentration, assuming perfect agreement at 0% ice
concentration. Currently, the NAM Model grid boxes
with less than 50% ice concentration are assigned sen-
VOLUME 47
FIG. 12. Flux observations averaged over 45-s intervals in flight
stack CD (gray dots), best-fit nonlinear curve (black, solid line),
and schematic representation of fluxes in some NWP models
(black, dotted line).
sible heat fluxes representative of open water (i.e., no
lake ice), while grid boxes with greater than 50% ice
concentration are assumed to be fully covered with 1-m
thick ice (Meteorology Education & Training 2006).
The observed nonlinear relationship suggests that the
sensible heat fluxes integrated over the entire range of
ice concentrations would be underestimated using
methods similar to the NAM Model. In fact, this underestimate in sensible heat fluxes would not be greatly
improved if a linear relationship between ice concentration and sensible heat fluxes were employed in mesoscale models.
5. Summary and future work
Analyses of data collected by the University of Wyoming King Air on 26 February 2004 during the Great
Lakes Ice Cover–Atmospheric Flux experiment revealed strong links between atmospheric conditions
and characteristics of partially pack ice–covered Lake
Erie. Observed low-level temperatures were found to
correlate more closely than mixing ratio to lake-surface
conditions. The close thermal link was also observed in
sensible and latent heat flux relationships with surface
ice concentration. It was shown that minor mesoscale
variations in surface and atmospheric thermodynamic
characteristics produced observable changes in heat
fluxes.
Sensible heat fluxes, an important driving mechanism
for lake-effect snow storms, were found to vary nonlinearly with surface ice concentrations. Near-open-water
fluxes were observed for ice concentrations less than
about 70%. This implies that if linear relationships are
employed in numerical weather prediction models, the
FEBRUARY 2008
GERBUSH ET AL.
total heating of the atmosphere by lakes with considerable pack ice cover would be significantly underestimated.
It is critical to determine whether these observed ice
concentration–heat flux relationships are common to
the Great Lakes and to examine their potential influence on mesoscale atmospheric responses. Collection
and analysis of field observations over a wide range of
atmospheric and surface pack ice conditions will give
necessary insight into both the statistical relationships
and the processes responsible for these relationships.
Given the observed links between atmospheric, lake,
and pack ice processes, interdisciplinary observational
field experiments and coupled modeling approaches
are needed to fully understand the interactions.
Acknowledgments. The authors greatly appreciate
the efforts of the staff and crew of the University of
Wyoming King Air. Forecasting for the GLICAF experiment was carried out by lead forecasters Michael
Kruk and Michael Spinar from the Illinois State Water
Survey, the authors, and Stephen Jackman from the
Department of Atmospheric Sciences, University of Illinois. Project assistance from Yarice Rodriguez, Department of Geography, University of Illinois, is also
appreciated. Internal reviews of the manuscript were
conducted by Jim Angel and Kenneth Kunkel from the
Illinois State Water Survey. Reviews by three anonymous reviewers are also appreciated. GLICAF and
analyses described here were funded by the National
Science Foundation (NSF 02-02305 and NSF 05-12954).
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the
National Science Foundation or the Illinois State Water
Survey.
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